Analytical Modeling of Magnetically Saturated Inductance by Lambert W Function

Abstract

Inductance is one of the most important components in order to make energy conversion in the power converters. The dynamics of power converter are affected by inductance. Therefore, in order to obtain accurate power converter dynamic model, one needs to have accurate inductance model. An inductance value is not always constant as it depends on current. Especially in the saturation region, inductance value decreases when current increases. On the other hand, exact eddy current and hysteresis losses estimation can be obtained with an accurate inductance model. This paper proposes an improved analytical inductance model that considers nonlinear B-H curve of a core material. A nonlinear B-H function is fitted using the Matlab Curve Fitting Toolbox. This function includes magnetic flux density (B) against magnetic field strength (H) variation in the both linear and saturation regions. The magnetic circuit model is obtained using a lumped parameter method and the Lambert W function is used to solve the equation which includes nonlinear core reluctance. In conclusion, a nonlinear analytical inductance model is proposed.